Cut off both ends of the oranges, then cut away the peel and bitter white pith. Over a small bowl to catch the juices, cut between the membrane and flesh to remove the orange segments.

On a large serving plate decoratively arrange the radicchio and arugula, alternating the colors, then top with the onions, orange segments and olives.

Whisk the olive oil and vinegar with the reserved orange juice to blend. Season to taste with salt and pepper, and drizzle over the salad. Top with crumbled goat cheese and serve.